System and method for improved waveform and enhanced receiver algorithm for high penetration alerting in a mobile satellite communications system

ABSTRACT

An approach is provided for high penetration alerting in a mobile satellite system. A message is generated for transmission to a wireless terminal. The message is partitioned into a number of symbols, each symbol composed of a portion of the message. The symbols are encoded via FEC coding to generate outer coded symbols, and each outer coded symbol is encoded based on a corresponding binary orthogonal sequence. The inner coded symbols are modulated based on a binary modulation scheme, and pulse shaped to generate message bursts for transmission to the wireless terminal. Each message burst reflects a group of the inner coded symbols, wherein the grouping of the inner coded symbols facilitates joint sequence detection by the wireless terminal, and each message burst exhibits relatively low peak-to-average power ratio.

RELATED APPLICATIONS

This application claims the benefit of the earlier filing date under 35U.S.C. §119(e) of U.S. Provisional Application Ser. No. 61/744,742(filed 3 Oct. 2012).

BACKGROUND

The present invention relates generally to mobile satellitecommunication systems, and more particularly to a method and system forproviding alert messaging to mobile terminals in high-attenuationpropagation environments within a mobile satellite communicationsnetwork.

Terrestrial communications systems continue to provide higher and higherspeed multimedia (e.g., voice, data, video, images, etc.) services toend-users. Such services (e.g., Third Generation (3G) and FourthGeneration (4G) services) can also accommodate differentiated quality ofservice (QoS) across various applications. To facilitate this,terrestrial architectures are moving towards an end-to-end all-InternetProtocol (IP) architecture that unifies all services, including voice,over the IP bearer. In parallel, mobile satellite systems (MSS) arebeing designed to complement and/or coexist with terrestrial coveragedepending on spectrum sharing rules and operator choice. With theadvances in processing power of desktop computers, the average user hasgrown accustomed to sophisticated applications (e.g., streaming video,radio broadcasts, video games, etc.), which place tremendous strain onnetwork resources. Internet services, as well as other IP services, relyon protocols and networking architectures that offer great flexibilityand robustness; however, such infrastructure may be inefficient intransporting IP traffic, which can result in large user response time,particularly if the traffic has to traverse an intermediary network witha relatively large latency (e.g., a satellite network). To promotegreater adoption of data communications services, the telecommunicationsindustry, from manufacturers to service providers, has agreed at greatexpense and effort to develop standards for communications protocolsthat underlie the various services and features.

Satellite systems, however, pose unique design challenges overterrestrial systems. That is, mobile satellite systems have differentattributes that make terrestrial designs either not applicable orinefficient for satellite systems. For example, satellite systems arecharacterized by long delays (as long as 260 ms one-way) between a userterminal device and a base station compared to the relatively shorterdelays (e.g., millisecond or less) in terrestrial cellular systems—whichimplies that protocols on the satellite links have to be enhanced tominimize impact of long propagation delays. Additionally, satellitelinks typically have smaller link margins than terrestrial links for agiven user-terminal power amplifier and antenna characteristics; thisimplies that higher spectral efficiency and power efficiency are neededin satellite links. Moreover, the satellite transmission or channelresources represent limited resources, where the deployment ofadditional transmission resources is significantly more expensive,difficult and time consuming as compared with terrestrial radioresources. Accordingly, the transmission resources of a satellite systemmust be used efficiently to maximize the available bandwidth, in orderto provide the required quality of service for the extensive and diverseassortment of service applications available to the mobile user, and tomaximize the number of potential users in a system without adverselyaffecting the quality of service.

Moreover, in mobile satellite communication systems, user terminals(UTs) (e.g., mobile terminals) typically employ a low gainomnidirectional antenna (e.g., of less than 6 dB gain). The antennacollects the transmission signal transmitted within the spot beam of anorbiting satellite, including the direct line-of-sight components of thesignal and the specular ground reflection components near the terminal.The antenna also collects multipath reflection components of the directsignal from taller stationary objects such as trees, mountains, andbuildings. Such reflection components can combine destructively whencollected, and result in attenuation or fading of the signal. Further,more severe signal fading or attenuation may occur if the line-of-sightpath between the mobile terminal and the orbiting satellite is blockedby a building or other object. This effect is called “shadowing.” Undercertain circumstances, therefore, where the shadowing and reflectivefactors may be enhanced (e.g., when the UT is within a metal-framedbuilding, underground or otherwise experiencing severe signal fading orattenuation), the UT might be unable to receive a paging or alert signaltransmitted by a network gateway via the satellite. The user or calledparty thus has no way of knowing that incoming calls are being lost.Accordingly, these factors contribute to lower success rates ofconventional mobile terminated calls.

To address the problems associated with shadowing and reflectivefactors, current mobile satellite systems employ an alerting method toprovide alert messaging to a mobile terminal being called, when the UTis within a heavily shadowed area. Alerting provides a high levelannouncement to a UT of a mobile terminated call, which provides theuser with a notification and the opportunity to move to a less heavilyshadowed area to receive the incoming call. Such an alerting method, asemployed by current mobile satellite systems, is described in U.S. Pat.No. 5,974,092, titled “Method and System For Mobile Alerting in ACommunication System.” Current mobile communications systems, however,utilize a 6 PSK modulated signal waveform in conjunction with aconventional orthogonal sequence, exhibiting high peak to average powerratio and irregular power spectrum, which prohibits efficient poweramplification. Such systems, therefore, fail to provide sufficient linkmargin to provide a reliable alert messaging approach undercircumstances of high attenuation. Moreover, the burst structure andcoding of such systems does not facilitate the use of joint sequencedetection in the receiver and forces the use of hard decision based FECdecoding. The alert message burst format of such current systems isdescribed in GMR-1 05.002 (ETSI TS 101 376-5-2): “GEO-Mobile RadioInterface Specifications; Part 5: Radio interface physical layerspecifications; Sub-part 2: Multiplexing and Multiple Access; Stage 2Service Description; GMR-1 05.002” (V-1.2.1) (hereinafter referred to as“ETSI TS 101 376-5-2”). The FEC channel coding employed in such currentsystems is described in GMR-1 05.003 (ETSI TS 101 376-5-3): “GEO-MobileRadio Interface Specifications; Part 5: Radio interface physical layerspecifications; Sub-part 3: Channel Coding; GMR-1 05.003” (V-1.2.1)(hereinafter referred to as “ETSI TS 101 376-5-3”). The modulated signalwaveform of such current systems is further described in the EuropeanTelecommunications Standards Institute (ETSI) publication GMR-1 05.004(ETSI TS 101 376-5-4): “GEO-Mobile Radio Interface Specifications; Part5: Radio interface physical layer specifications; Sub-part 4:Modulation; GMR-1 05.004” (V-1.2.1) (hereinafter referred to as “ETSI TS101 376-5-4”). Accordingly, the system and method of alert messaging incurrent mobile satellite communications systems fails to provide foroptimal waveforms for high penetration alerting, and for receiveralgorithms that facilitate joint sequence detection and soft decisiondecoding.

What is needed, therefore, is an approach for high penetration alertingin a mobile satellite communications system that employs an enhancedwaveform design that exhibits lower peak-to-average power ratio andpermits joint sequence detection. What is also needed, therefore, is andapproach for high penetration alerting in a mobile satellitecommunications system that employs an enhanced receiver algorithm thatfacilitates computationally efficient joint sequence detection and softdecision decoding.

SOME EXEMPLARY EMBODIMENTS

The present invention advantageously addresses the foregoingrequirements and needs, as well as others, by providing a system andmethod for reliable high penetration alerting in a mobile satellitecommunications system that employs an enhanced waveform design anenhanced receiver algorithm. The enhanced waveform, in accordance withexemplary embodiments of the present invention, exhibits lowerpeak-to-average power ratio and permits joint sequence detection.Further, the enhanced receiver algorithm, in accordance with exemplaryembodiments of the present invention, facilitates computationallyefficient joint sequence detection and soft decision decoding. Accordingto exemplary embodiments, the present invention thereby provides for areliable means for high penetration alerting, based on improved linkmargins due to enhanced waveform designs and receiver algorithms, forproviding alert signal messaging to user terminals situated in highlypower attenuated locations.

According to an example embodiment, a method comprises generating amessage for transmission to a wireless terminal, wherein the messagecomprises a number of bits. The message is partitioned into a number ofsymbols, each symbol being composed of a distinct equal length portionof the message. The symbols are encoded via an FEC outer coding togenerate a number of outer coded symbols, and each of the outer codedsymbols is encoded based on an orthogonal sequence inner coding togenerate a respective inner coded symbol, wherein each outer codedsymbol is coded based on a distinct corresponding one of a plurality ofbinary orthogonal sequences. The inner coded symbols are modulated basedon a binary modulation scheme, and pulse shaped to generate a pluralityof message bursts for transmission to the wireless terminal. Eachmessage burst reflects a group of a uniform number of the inner codedsymbols, wherein the grouping of the inner coded symbols within themessage bursts facilitates joint sequence detection by a receiver of thewireless terminal, and wherein each message burst exhibits relativelylow peak-to-average power ratio. Further, the distinct correspondingbinary orthogonal sequence, based upon which each outer coded symbol isencoded, is based on a value of the respective outer coded symbol,wherein each outer coded symbol is four bits in length, and theorthogonal sequence inner coding comprises a 16-ary coding based onsixteen binary orthogonal sequences with each sequence corresponding toa respective one of the potential four-bit values of the outer codedsymbols. Additionally, the encoding of the outer coded symbols mayfurther comprise scrambling each message burst based on a binaryscrambling sequence. According to one embodiment, the message comprises36 information bits, the message is partitioned into nine 4-bit symbols,the FEC outer coding generates fifteen 4-bit outer coded symbols, eachmessage burst reflects a group of three of the inner coded symbols, andthe binary modulation scheme comprises a π/2 BPSK scheme.

According to a further example embodiment, an apparatus comprises aprocessor module configured to generate a message for transmission to awireless terminal, wherein the message comprises a number of bits, andto partition the message into a number of symbols, each symbol beingcomposed of a distinct equal length portion of the message. Theapparatus further comprises an encoder module configured to encode thesymbols via an FEC outer coding to generate a number of outer codedsymbols, and to encode each of the outer coded symbols based on anorthogonal sequence inner coding to generate a respective inner codedsymbol, wherein each outer coded symbol is coded based on a distinctcorresponding one of a plurality of binary orthogonal sequences. Theapparatus also comprises a modulator module configured to modulate theinner coded symbols based on a binary modulation scheme, one or morepulse shaping filters to pulse shape the modulated inner coded symbolsto generate a plurality of message bursts for transmission to thewireless terminal. Each message burst reflects a group of a uniformnumber of the inner coded symbols, wherein the grouping of the innercoded symbols within the message bursts facilitates joint sequencedetection by a receiver of the wireless terminal, and wherein eachmessage burst exhibits relatively low peak-to-average power ratio.Further, the distinct corresponding binary orthogonal sequence, basedupon which each outer coded symbol is encoded, is based on a value ofthe respective outer coded symbol, wherein each outer coded symbol isfour bits in length, and the orthogonal sequence inner coding comprisesa 16-ary coding based on sixteen binary orthogonal sequences with eachsequence corresponding to a respective one of the potential four-bitvalues of the outer coded symbols. Additionally, the encoding of theouter coded symbols may further comprise scrambling each message burstbased on a binary scrambling sequence. According to one embodiment, themessage comprises 36 information bits, the message is partitioned intonine 4-bit symbols, the FEC outer coding generates fifteen 4-bit outercoded symbols, each message burst reflects a group of three of the innercoded symbols, and the binary modulation scheme comprises a π/2 BPSKscheme.

Still other aspects, features, and advantages of the invention arereadily apparent from the following detailed description, simply byillustrating a number of particular embodiments and implementations,including the best mode contemplated for carrying out the invention. Theinvention is also capable of other and different embodiments, and itsseveral details can be modified in various obvious respects, all withoutdeparting from the spirit and scope of the invention. Accordingly, thedrawings and description are to be regarded as illustrative in nature,and not as restrictive.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is illustrated by way of example, and not by wayof limitation, in the figures of the accompanying drawings, and in whichlike reference numerals refer to similar elements, and wherein:

FIGS. 1A and 1B illustrate diagrams of communications systems capable ofproviding Internet Protocol (IP)-based communications sessions from aterrestrial (wireline or wireless) domain to a satellite domain,according to various exemplary embodiments;

FIG. 2 illustrates an exemplary composite waveform resulting from anexemplary dual-chirp waveform synchronization burst, in accordance withexemplary embodiments;

FIG. 3 illustrates FEC coding of an alert message (e.g., of 36information bits) for transmission as five alert message bursts, inaccordance with an exemplary embodiment;

FIG. 4 illustrates an exemplary implementation of an encoding algorithmin the form of a feedback shift register, in accordance with anexemplary embodiment;

FIG. 5 illustrates an exemplary alert message burst, reflecting threemodulated orthogonal sequences, of a time duration of 10 ms at thetransmission rate of 23.4 ksps, in accordance with an exemplaryembodiment;

FIG. 6 illustrates a time distributed signal transmission of theSynchronization Burst and Alert Message Bursts, in accordance with anexemplary embodiment;

FIG. 7 illustrates a block diagram of a demodulator and decoder of a UTor mobile terminal receiver, in accordance with an exemplary embodiment;

FIG. 8 illustrates an exemplary process whereby the mobile terminal orUT receiver acquires initial timing and frequency based on thesynchronization burst, in accordance with an exemplary embodiment,

FIG. 9A illustrates a synchronization burst tracking algorithm, inaccordance with an exemplary embodiment;

FIG. 9B illustrates a 2nd order loop that can be used to track thefrequency and timing individually, in accordance with an exemplaryembodiment;

FIG. 10A illustrates a flow chart depicting an iterative erasure-baseddecoding process, in accordance with an exemplary embodiment;

FIG. 10B illustrates an RS decoding process employing a conventionalEuclidian algorithm, in accordance with an exemplary embodiment;

FIG. 11A illustrates a power spectrum density (PSD) plot of an alertmessage burst which has been coded utilizing a Reed-Solomon outer codingand an orthogonal sequence with scrambling, in accordance with anexemplary embodiment;

FIG. 11B illustrates a power spectrum density (PSD) plot of an alertmessage burst which has been coded utilizing a Reed-Solomon outer coding(in accordance with an exemplary embodiment) and a conventionalorthogonal sequence without scrambling;

FIG. 11C illustrates a performance plot of a frequency tracking loopimplemented in accordance with an exemplary embodiment;

FIG. 11D illustrates a performance plot of a timing tracking loopimplemented in accordance with an exemplary embodiment;

FIG. 11E illustrates a plot of the sequence error detection performance,over an AWGN channel, comparing the performance variations between theoptimal use of all 16 candidates in the joint detection against use of 5candidates and 3 candidates, in accordance with exemplary embodiments;

FIG. 11F illustrates a plot of the alert message error performance,comparing the alert message error rates between an exemplary embodimentand the conventional alert messaging approach;

FIG. 12 illustrates a block diagram of exemplary components of a userterminal configured to operate in the systems of FIGS. 1A and 1B,according to an exemplary embodiment;

FIG. 13 illustrates a chip set with respect to which embodiments of theinvention may be implemented; and

FIG. 14 illustrates a block diagram of hardware that can be used toimplement certain exemplary embodiments.

DETAILED DESCRIPTION

A system and method for reliable high penetration alerting in a mobilesatellite communications system, which employs an enhanced waveformdesign an enhanced receiver algorithm, are provided. In the followingdescription, for the purposes of explanation, numerous specific detailsare set forth in order to provide a thorough understanding of theembodiments of the invention. It is apparent, however, to one skilled inthe art that the embodiments of the invention may be practiced withoutthese specific details or with an equivalent arrangement. In otherinstances, well-known structures and devices are shown in block diagramform in order to avoid unnecessarily obscuring the embodiments of theinvention.

FIGS. 1A and 1B illustrate diagrams of communications systems capable ofproviding Internet Protocol (IP)-based communications sessions from aterrestrial (wireline or wireless) domain to a satellite domain,according to various exemplary embodiments. For the purposes ofillustration, a system 100 of FIG. 1A supports multimedia services usingan Internet Protocol (IP) architecture, such that end-to-endcommunications sessions are packetized. By way of example, a terrestrialcore network (CN) 101 is a wireless core network that is compliant witha Third Generation (3G) or Fourth Generation (4G) architecture; e.g.,Third Generation Partnership Project (3GPP)-based. For example, thesystem 100 can utilize a satellite air interface denoted as GMR-1 3G,which is an evolution of the GMR-1 air interface standards; GMR-1 3G hasbeen adopted as a mobile satellite system standard by the EuropeanTelecommunications Standards Institute (ETSI) and the InternationalTelecommunications Union (ITU). The wireless core network 101 may alsohave connectivity to a data network 103 and a telephony network 105.

Networks 101, 103, and 105 may be any suitable wireline and/or wirelessnetwork. For example, telephony network 105 may include acircuit-switched network, such as the public switched telephone network(PSTN), an integrated services digital network (ISDN), a private branchexchange (PBX), an automotive telematics network, or other like network.Wireless network 101 (e.g., cellular system) may employ varioustechnologies including, for example, code division multiple access(CDMA), enhanced data rates for global evolution (EDGE), general packetradio service (GPRS), global system for mobile communications (GSM), IPmultimedia subsystem (IMS), universal mobile telecommunications system(UMTS), etc., as well as any other suitable wireless medium, e.g.,microwave access (WiMAX), wireless fidelity (WiFi), satellite, and thelike. Moreover, data network 103 may be any local area network (LAN),metropolitan area network (MAN), wide area network (WAN), the Internet,or any other suitable packet-switched network, such as a commerciallyowned, proprietary packet-switched network having voice over InternetProtocol (VoIP) capabilities, e.g., a proprietary cable or fiber-opticnetwork.

Within the satellite domain, a satellite base station subsystem (SBSS)107 is introduced that implements the necessary modifications andenhancements for efficient operation over a satellite 109 to one or moreuser terminals 111 a-111 n. These terminals 111 a-111 n can be ofvarious types with different form factors and transmit capabilities;e.g., sleek hand-held terminals, personal digital assistants (PDAs),vehicular terminals, portable terminals, fixed terminals, automotivetelematics terminals, etc.

The SBSS 107 communicates with the wireless network 101, which includesa core network (e.g., 3G/4G) that is unchanged from terrestrial corenetwork. This consequently permits operators to reuse existing 3G/4Gcore network elements. The interface between the SBSS 107 and the 3G/4Gcore network 101 can be a standard terrestrial interface. Again, a 3Gnetwork interfaces with the 3G/4G CN 101 to transmit IP packets toexternal networks such as the internet. The CN 101 includes a ServingGPRS Support Node (SGSN) 121 and a Gateway GPRS Support Node (GGSN) 123.The SGSN 121 is generally operable to transfer data packets to and fromUT 111 within its geographical area. Some of the non-limiting functionsof SGSN 121 include packet routing and transfer, authentication andcharging functions of GPRS mobiles, mobility management and logical linkmanagement. A location register of the SGSN 121 stores locationinformation (for example, current cell, current Visitor LocationRegister) and user profiles of all GPRS users registered with the SGSN121. The GGSN 123 is responsible for sending user packets to external IPbased networks and routing packets back to the mobile user. GGSN 123 isoperable to convert GPRS packets coming from SGSN 121 into theappropriate Packet Data Protocol (PDP) format and sends them out tocorresponding packet data network. GGSN 123 has several functions,including packet inspection for detecting different types for traffic,which can be used for shaping the traffic under different network loadconditions. GGSN 123 keeps a record of active mobile users attached toSGSN 121. GGSN 122 is also responsible for policy control, billing andassigning IP addresses to mobile users. When GGSN 123 receives dataaddressed to a specific user routed through the CN 101, it checks if theuser is active. For example, if UT 111 is active, GGSN 123 forwards thedata to SGSN 121, and if UT 111 is not active, the data are discarded.

It is also noted that the architecture of the system 100 permits thesame core network element to simultaneously communicate with aterrestrial base station (not shown) and the SBSS 107. This capabilityis illustrated in FIG. 1B. As seen, the system 100 enables handoverprocedures between terrestrial base-station and the SBSS 107 to beexecuted via a core network 101 with standard procedures defined interrestrial systems. In this example, the UT 111 has the capability tocommunicate over a satellite link or directly communicate with aterrestrial radio access network (RAN) 113 to the wireless core network(CN) 101. The RAN 113 comprises a radio network controller (RNC) 125,which is responsible for the radio resource management functions andcertain mobility management functions of the network. By way of example,the data network 103 is configured as an IP/IMS (IP MultimediaSubsystem) with multiple application servers 115 supplying multimediacontent. The data network 103 couples to the PSTN 105 via a mediagateway 117; the PSTN 105 can serve one or more voice terminals 119.

The following describes the signal transmission design for thesynchronization burst and alert message burst, in accordance withexemplary embodiments of the present invention. The synchronizationburst uses a dual chirp waveform methodology, and does not carry anymessage information. The characteristics of a dual chirp waveform (withrespect to the synchronization burst of prior systems) are described inU.S. Pat. No. 6,418,158 (hereinafter referred to as “U.S. Pat. No.6,418,158”), titled “Synchronization in Mobile Satellite Systems UsingDual-Chirp Waveform,” the entirety of which is incorporated by referenceherein. The dual chirp waveform is further described in ETSI TS 101376-5-4. The alert message burst is modulated and FEC encoded. Thecharacteristics of the alert message burst format and channel codingemployed in prior systems is described in ETSI TS 101 376-5-2 and ETSITS 101 376-5-3, respectively. While the synchronization bursts and alertmessage bursts may be transmitted via different carriers, asynchronization message burst should be transmitted proximal to therespective alert message burst. In accordance with one exemplaryembodiment, both the synchronization bursts and alert message bursts aretransmitted on the same carrier in a time division multiplexed manner.

Transmission

Synchronization Burst Signal.

In accordance with an exemplary embodiment, the synchronization messageburst is transmitted uncoded via a dual-chirp waveform. By way ofexample, the representation of a synchronization burst transmitted witha dual-chirp waveform, having a frequency sweeping rate of ±7.488 kHz,over a 20 ms interval adopted for the chirp transmission at thetransmission rate of 23.4 ksps may be represented as:

cos(μπ(t−0.5NT _(s))²),

-   -   where μ=2λ/NT_(s) ², N=468, T_(s)=(1/23.4)ms, and λ=0.32.        FIG. 2 illustrates an exemplary composite waveform resulting        from an exemplary dual-chirp waveform synchronization burst, in        accordance with exemplary embodiments. The composite waveform        depicted in FIG. 2 is referred to as a dual-chirp waveform,        because it is a composite waveform consisting of two component        waveforms: an up-chirp waveform and a down-chirp waveform. A        chirp waveform is a signal in which the frequency changes        linearly over the duration of the waveform, or, in other words,        the frequency sweeps (the frequency varies with time) across the        duration of the chirp waveform. Accordingly, a chirp waveform is        in contrast to a sinusoidal or tone waveform, in which the        frequency remains constant throughout the duration of the        waveform. The dual-chirp waveform is a composite of an up-chirp        waveform and a down-chirp waveform, where the up-chirp waveform        has a frequency that increases linearly with time, and the        down-chirp waveform has a frequency that decreases linearly with        time. Advantageously, the frequency of the up-chirp waveform and        the down-chirp waveform vary oppositely with respect to time,        which facilitates detection at the receiver, for example, using        a Fast Fourier Transform (FFT).

Alert Message Burst Signal.

An alert message burst may be employed to send an alert message tosignificantly disadvantaged (e.g., power attenuated) terminals.According to exemplary embodiments, the physical characteristics of analert message burst include: (1) 36 information bits; (2) FEC outercoding in the form of a Reed-Solomon (15,9) code; (3) rt/2 BPSKmodulation; (4) pulse shaping; and (5) transmission as a coded messageof 5 alert message bursts. As a result, an alert message block of 36information bits is transmitted via five alert message bursts.

Alert Message:

FIG. 3 illustrates FEC coding of an alert message 311 (e.g., of 36information bits) for transmission as five alert message bursts 325, inaccordance with an exemplary embodiment. Each of the five alert messagebursts 325 reflects three coded 4-bit symbols of the alert message 311.By way of example, an alert message block d(k) (of 36 information bits)311 is first multiplexed into nine 4-bit symbols 313, to produce 9×4data blocks D, with the elements d(i, j) defined as:

d(i,j)=d(k),

-   -   where k=0, 1, . . . 35; i=INT(k/4), and j=k mod 4.

FEC Outer Coding:

The FEC encoding 315 is then applied to each 4-bit symbol in the datablock D. By way of example, the FEC encoding comprises a Reed-Solomon(15,9) outer code, with a Galois field of 2⁴ (GF(2⁴)). The Reed-Solomonencoding adds parity check symbols to produce fifteen 4-bit symbols 317,resulting in a 15×4 data block C with the elements c(i,j). Thesystematic (15,9) Reed-Solomon (RS) code, generated over the Galoisfield GF(2⁴), is used to encode blocks of 9 information symbols (of 4bits each) into a block of 15 coded symbols. The Galois field GF(2⁴) maybe defined with a as its primitive element under an irreduciblepolynomial:

p(X)=1+X+X ⁴.

The generator polynomial G(X) may be defined as:

G(X)=g ₀ +g ₁ X+g ₂ X ² +g ₃ X ³ +g ₄ X ⁴ +g ₅ X ⁵ +X ⁶

The (15,9) Reed-Solomon encoder thereby computes and adds six errorcorrection symbols (parity symbols) to the block of 9 informationsymbols, resulting in the fifteen 4-bit symbols 317, where each alertmessage burst 325 reflects three Reed-Solomon symbols, and where slottedtransmission provides time diversity. Such an FEC outer codingmethodology results in a robust coded signal with respect to burstyerrors.

FIG. 4 illustrates an exemplary implementation of an encoding algorithmin the form of a feedback shift register, in accordance with anexemplary embodiment. The register (b₀-b₆) is initially loaded withzeros. When the input message symbols (w₀-w₈) arrive, they are deliveredto the output symbols (w₀-w₈) and simultaneously added to b₅, to serveas the common feedback symbols. At each tap, the feedback symbol ismultiplied by the respective tap coefficient (g₀-g₅). The product isthen available at each tap for the shift operation, where the shiftbegins at the output end, using the previous register values.Specifically, symbol b₅ is shifted to b₆, and b₄ is added to thefeedback result and stored in b₅. This process continues until finallyb₀ is loaded with its new value. For the output symbols (w₉-w₁₄), a zerois asserted as the feedback symbols, and the register contents areshifted to the output. The shift occurs before the output is taken. Asan alternate implementation, the register could be read out in order(b₅-b₀) for the (w₉-w₁₄) symbol outputs.

Each 4-bit RS coded symbol 317 is then coded based on an inner coding319. By way of example, a 16-ary orthogonal sequence inner coding isapplied based on binary orthogonal sequences, as follows:

Sequence Sequence Elements (76 per each Sequence) S00001001100001111001100000000111111001111111100111111000000001100111100001100S10011000100110000111100110000000011111100111111110011111100000000110011110000S20000001100010011000011110011000000001111110011111111001111110000000011001111S30011110000110001001100001111001100000000111111001111111100111111000000001100S40011001111000011000100110000111100110000000011111100111111110011111100000000S50000001100111100001100010011000011110011000000001111110011111111001111110000S60000000000110011110000110001001100001111001100000000111111001111111100111111S70011110000000011001111000011000100110000111100110000000011111100111111110011S81111000000111111110011000011110011101100111100001100111111110000001100000000S91100001100000011111111001100001111001110110011110000110011111111000000110000S101100000000110000001111111100110000111100111011001111000011001111111100000011S111100110000000011000000111111110011000011110011101100111100001100111111110000S121100000011000000001100000011111111001100001111001110110011110000110011111111S131111110000001100000000110000001111111100110000111100111011001111000011001111S141111111111000000110000000011000000111111110011000011110011101100111100001100S151111001111111100000011000000001100000011111111001100001111001110110011110000Further, each of the 4 RS coded bits 317 (i.e., one RS symbol) is mappedto a respective one of the 16 sequences S_(j), as follows:

Coded Bits {c(i, 0), . . . c(i, 3)} Sequence S_(j) 0000 S₀ 0001 S₁ 0010S₂ 0011 S₃ 0100 S₄ 0101 S₅ 0110 S₆ 0111 S₇ 1000 S₈ 1001 S₉ 1010 S₁₀ 1011S₁₁ 1100 S₁₂ 1101 S₁₃ 1110 S₁₄ 1111 S₁₅The three concatenated sequences of each alert message burst are thenscrambled by a binary scrambling sequence of length 228, as follows:

-   -   0001001100011011110001000010010100001111100011000001010111101111    -   1100110101101010111011001001100101101110001000110110100001111011    -   0110000010100100100000011000111000000010000101111111100000110101    -   010111111011001100101010010001000110        For example, the first scrambling bit is scrambled with the        first bit of first orthogonal sequence in the burst, and the        last scrambling bit is scrambled with the last bit of the third        orthogonal sequence in the burst. A bit for one idle symbol at        the end of each burst is set to 0 with no scrambling.

Modulation:

The scrambled sequences are then modulated 321. By way of example, a π/2BPSK modulation scheme is employed, as follows:

S _(l)=(−1)^(d) ^(l) *e ^(jl(π/2))

-   -   where d₁ denotes the scrambled bits, and S_(l) denotes the π/2        BPSK modulated symbol.

Pulse Shaping: The complex valued modulated symbols are filtered, forexample via a pulse shaping filter 323, prior to transmission. By way ofexample, a square root raised cosine filter with roll off factor 0.35 isapplied for pulse shaping, as follows:

${h(t)} = {\frac{{T_{s}^{2}/4}\; \alpha}{\pi \left( {\left( {{T_{s}/4}\; \alpha} \right)^{2} - t^{2}} \right)}\left\{ {{\cos \left( \frac{\left( {1 + \alpha} \right)\pi \; t}{T_{s}} \right)} + {\frac{T_{s}}{4\; \alpha \; t}{\sin \left( \frac{\left( {1 - \alpha} \right)\pi \; t}{T_{s}} \right)}}} \right\}}$

-   -   where α=0.35 is the roll-off factor of the pulse shaping filter,        and        -   T_(s)=1/23,400 is the symbol duration in seconds.            The burst can be represented by:

${x(t)} = {{g(t)}\left\{ {\sum\limits_{k = 0}^{N - 1}\; {s_{k}{h\left( {t - T_{s}} \right)}}} \right\}}$

-   -   where N=234 is the number of symbols in the burst, and    -   g(t) is the time window function that controls the burst ramping        up and down.        For example, each alert message burst, reflecting three π/2 BPSK        modulated scrambled orthogonal sequences, may be of a time        duration of 10 ms at the transmission rate of 23.4 ksps, as        depicted in FIG. 5.

Multiplexing of Synchronization Burst and Alert Message Burst.

In accordance with an exemplary embodiment, the Synchronization Burstsand Alert Message Bursts are transmitted according to a time distributedtransmission over the same carrier. By way of example, thesynchronization burst is periodically transmitted (e.g., the network maytransmit a synchronization burst of a 20 ms duration every 320 ms).Additionally, a single alert message is transmitted over a number ofalert message bursts (e.g., alert message 311 transmitted over the fivealert message bursts 325, as illustrated in FIG. 3), where each burst,for example, is of a duration of 10 ms. Further, to achieve furtherefficiencies, multiple UTs 111 (e.g., mobile terminals) can be alertedvia a single carrier using multiple alert groups (Alert Groups or AGs)of alert message bursts. A mobile terminal thus need only monitor aparticular AG to which it is assigned. Accordingly, various benefits arerealized by such multiplexing of synchronization and alert messages. Forexample, once synchronized, a mobile terminal need only monitor thepre-assigned time slots for the respective alert group assigned to theterminal, which conserves mobile terminal battery life, and timediversity gain in the presence of multi-path fading reduces fadingmargin requirements.

FIG. 6 illustrates a time distributed signal transmission of theSynchronization Burst and Alert Message Bursts, in accordance with anexemplary embodiment. As illustrated in FIG. 6, alert messages aretransmitted to a batch group of eight different alert groups {AG0, AG1,. . . AG6, AG7} over a period of 2560 ms (2.56 seconds), where eachalert group transmission (AG(x)) comprises the five alert message burstsof the respective alert message. A particular UT 111 will look at thealert message of the five alert message bursts transmitted at the timeslot of the respective alert group to which that terminal is assigned.Further, a synchronization burst (SB) is transmitted at the beginning ofeach 320 ms interval, and each UT will monitor (wake up for) every SB.Within this 2.56 second time period, each UT will know within which 320ms SB periods to look for the alert message bursts associated with thealert group assigned to the UT, and will know the time slot within thoseparticular 320 ms SB periods to acquire the respective alert messagebursts.

More specifically, prior to entering the alerting mode, a UT will havecompleted a system-level synchronization. During the system levelsynchronization, the UT receives certain system information via a systeminformation broadcast, including acquisition of system-level frame andframe number synchronization (and slot synchronization within theframes). Further, the system information provides the UT with thelocation of the synchronization bursts and the respective alert grouplocations (in the time domain) as a function of the frame and slotnumber. Based on the frame synchronization, the UT maintains an internalclock, and thereby knows when to wake up for each synchronization burst,and (with respect to each SB) where the particular alert burst locationsare within each 320 ms SB period. Accordingly, the synchronizationbursts enable the UT to maintain timing and frequency synchronization,and enable the UT to locate the alert group transmissions assigned toit, in relation to the respective synchronization bursts.

Reception

The UT 111 (e.g., mobile terminal) acquires time and frequencysynchronization with the incoming transmissions from the network. Oncetime and frequency synchronized, the mobile terminal can demodulate thealert message bursts and decode and reassemble the alert message. Thecharacteristics of the synchronization burst acquisition and trackingprocess, as employed in prior systems, is described in U.S. Pat. No.6,418,158. The following describes the synchronization burst acquisitionand tracking process of exemplary embodiments of the present invention.

FIG. 7 illustrates a block diagram of a demodulator and decoder of a UTor mobile terminal receiver, in accordance with an exemplary embodiment.The demodulator demodulates the synchronization bursts and alert messagebursts received by the terminal. As depicted in FIG. 7, the demodulatorcomprises an SQRC matched filter 711, a sample interpolator anddecimation module 713, a frequency and timing estimation and trackingmodule 715, a timing and frequency compensation module 717, a π/2de-rotation and descrambling module 719, a joint sequence detectionmodule 721 and associated orthogonal sequence module 723, an SNRestimation and decoder input generation module 725, and a buffer module727.

As will be appreciated, a module or component (as referred to herein)may be composed of software component(s), which are stored in a memoryor other computer-readable storage medium, and executed by one or moreprocessors or CPUs of the respective devices. As will also beappreciated, however, a module may alternatively be composed of hardwarecomponent(s) or firmware component(s), or a combination of hardware,firmware and/or software components. Further, with respect to thevarious exemplary embodiments described herein, while certain of thefunctions are described as being performed by certain components ormodules (or combinations thereof), such descriptions are provided asexamples and are thus not intended to be limiting. Accordingly, any suchfunctions may be envisioned as being performed by other components ormodules (or combinations thereof), without departing from the spirit andgeneral scope of the present invention.

Synchronization Burst Acquisition.

During acquisition at the UT 111, an acquisition system within theterminal searches a pre-defined set of carriers (e.g., searches 10channels of approximately 1000 available channels) for thesynchronization burst (e.g., the dual-chirp waveform, as describedabove). Once located, the UT utilizes the dual-chirp waveform (e.g., asdepicted in FIG. 2) to determine the associated frequency offset andtiming offset, which is used to compute the carrier frequency and frametiming information (e.g., for communications to the gateway or SBSS 107via the satellite 109). The UT thereby has completed acquisition of thesynchronization burst, and is thus synchronized with the gateway or SBSS107.

FIG. 8 illustrates an exemplary process whereby the mobile terminal orUT receiver acquires initial timing and frequency based on thesynchronization burst, in accordance with an exemplary embodiment. Byway of example, the receiver acquisition process uses a total searchwindow of 340 ms, which equates to the synchronization bursttransmission period (e.g., 320 ms) plus the synchronization burstduration (e.g., 20 ms). The burst acquisition is performed based on asliding window buffer of 20 ms, with a 2.5 ms shift, which results in atotal of 129 overlapped buffers in the 340 ms search window.

For each 20 ms buffer window, the following describes thesynchronization burst acquisition and tracking process, as depicted inFIG. 8. First, a 20 ms matched filter output is captured (4samples/symbol), corresponding to 4*4*117=1872 complex samples. The Iand Q signals are then decimated by a factor of two, resulting in2*4*117=936 complex samples. A desweeping with respect to the up-chirp,for the 936 complex samples, as follows: exp(−μπ(t−0.5NT_(s))²). Theneighty-eight complex zeros are added to the 936 complex samples to make1024 complex samples for Fast Fourier Transform (FFT) processing. Basedon the FFT output, signal-to-noise ratio (SNR) and frequency estimationare performed, and the SNR and up-chirp frequency estimation (f_est_up)are recorded for each buffer window. More specifically, the SNR andfrequency estimation comprise the following steps:

-   -   1. Find the frequency bin that gives the maximum |FFT|² and        denote it as f_est_up.    -   2. Perform signal power computation, as follows:

Ps=(|FFT(f_est_up)|²+|FFT(f_est_up_left)|²+|FFT(f_est_up_right)|²)/3

-   -    where f_est_up_left and f_est_up_right are the closest neighbor        bins left and right of f_est_up, respectively.    -   3. Perform noise power computation, as follows:

Pn=(sum of |FFT|² for the other 1024 bins)/(1024)

-   -   4. Compute the SNR as SNR=10 log(Ps/Pn).

If the estimated SNR is larger than a predefined detection threshold(e.g., 10 dB) for a predefined maximum consecutive buffers (e.g.,max_consecutive=4 continuous buffers), then detection of the burst isset. This process is repeated until the end of the 340 ms search window,and the estimated SNR and its corresponding f_est_up are updated withthe highest SNR during the 340 ms search. Then, for the buffer detectedwith the highest SNR, a desweeping is performed with respect to thedown-chirp, for the 936 complex samples, as follows:exp(−μπ(t−0.5NT_(s))²). Again, eighty-eight complex zeros are added tothe 936 complex samples to make 1024 complex samples for Fast FourierTransform (FFT) processing. Based on the FFT output, signal-to-noiseratio (SNR) and frequency estimation are performed, and the SNR anddown-chirp frequency estimation (f_est_up) are recorded for each bufferwindow. More specifically, the SNR and frequency estimation comprise thefollowing steps:

-   -   1. Find the frequency bin that gives the maximum |FFT|² and        denote it as f_est_down.    -   2. Perform signal power computation, as follows:

Ps=(|FFT(f_est_down)|²+IFFT(f_est_down_left)|²+IFFT(f_est_down_right)|²)/3

-   -    where f_est_down_left and f_est_down_right are the closest        neighbor bins left and right of f_est_down, respectively.    -   3. Perform noise power computation, as follows:

Pn=(sum of |FFT|² for the other 1024 bins)/(1024)

-   -   4. Compute the SNR as SNR=10 log(Ps/Pn).

If the estimated SNR with respect to the down-chirp is also larger thanthe predefined detection threshold (e.g., 10 dB), the synchronizationburst is determined as being present in the respective buffer, and thefreq_est_down is recorded (which gives the maximum). Otherwise, it isdetermined that no burst has been detected in the 340 ms search window.This situation may arise, for example, when the presence of noise and/orother interference prevents the receiver from detecting thesynchronization burst in a particular 320 ms synchronization burstperiod. Once the synchronization burst is detected, the frequency andtiming shifts are computed, as follows:

freq_offset_est=(freq_est_up+freq_est_down)/2.0

time_offset_est=(freq_offset_est−freq_est_up)/μ.

In accordance with a further exemplary embodiment, a three-pointLagrange interpolator may be used to enhance the frequency estimation.

Synchronization Burst Tracking.

The following describes the time and frequency tracking algorithm, for adual chirp synchronization burst waveform, in accordance with anexemplary embodiment. By way of example, the following table summarizesthe receiver parameters for synchronization tracking:

Module Parameter Values SQRC Matched Number of symbols per burst: N =468 Filtering Roll-off factor: α = 0.35; Filter window size: (Module711) L = 8 symbols Number of samples per symbol: M = 4 Timing ErrorNumber of samples per symbol: M = 4 before Compensation interpolationInterpolation and Interpolation filter tap length: I = 16 DecimationOversampling factor for interpolation: v = 8 (Module 713) FrequencyError Number of samples per symbol: M = 2 Compensation and De-chirpingapplies to both up-chirp and down-chirp De-Chirping Frequency correctionfrom tracking loop is also (Module 717) applied during de-chirpingFrequency and Number of samples per symbol: M = 2 Timing Error 1024point FFT for both up and down chirps Estimation Consider only adjacent±2 FFT bins from the (Module 715) tracking frequency (total 5 hypothesistesting) for maximum correlation peak search. Frequency and timing errorsignals are generated by adding and subtracting up and down chirp FFTfrequency estimate, respectively. Frequency and 2^(nd) order trackingloop for timing Timing and frequency individually Tracking Loop (Module715)

According to an exemplary embodiments of the present invention, thefrequency and timing offset error generation follows the equationsdescribed above, namely:freq_offset_est=(freq_est_up+freq_est_down)/2.0, andtime_offset_est=_(— —) (freq_offset_est−freq_est_up)/μ. However, basedon various advantages or improvements achieved via such exemplaryembodiments, a majority of frequency and timing uncertainly is removedduring the initial synchronization acquisition process, and thus thefrequency and timing uncertainty in the synchronization tracking mode isgreatly reduced from that of the initial acquisition phase. Hence,according to a further exemplary embodiment, the number of FFT bins usedfor the correlation peak search can be reduced from 1024 bins to 5 binscentered around the tracked frequency. This reduction in the number ofFFT bins used for the correlation peak search results in a minimizationof the receiver detecting wrong FFT frequency bins, and improvesfrequency and timing tracking performance. Further, the reduction in thenumber of FFT bins also results in a reduction of computation complexityand time for the synchronization tracking process.

FIG. 9A illustrates a synchronization burst tracking algorithm, inaccordance with an exemplary embodiment, and FIG. 9B illustrates a 2ndorder loop that can be used to track the frequency and timingindividually, in accordance with an exemplary embodiment. By way ofexample, the equivalent equations for the loop filter of FIG. 9B may bereflected as:

x(n)=d(n−1)+γ_(l) e(n)

d(n)=d(n−1)+γ₂ e(n)

y(n)=y(n−1)+x(n)

The coefficient γ_(i) is the first order parameter, which defines thelength of the averaging window, and is thus directly related to thebandwidth of the loop. The coefficient γ₂ is the second order parameter,which acts like a gain on the stochastic estimate of the drift. Thedetermination of the γ₁ and γ₂ values sets a tradeoff between drifttracking and averaging, and are performed using simulation. Further, thefollowing table reflects exemplary frequency and timing tracking filtercoefficients:

γ₁ γ₂ Frequency Tracking Filter 0.55 0.000250 Timing Tracking Filter0.05 0.002

Demodulation.

As mentioned above, the demodulator of the UT 111 (e.g., the demodulatorillustrated in FIG. 7) demodulates the alert message burst signals (aswell as the synchronization burst signals) received by the terminal. Aswould be well recognized and understood by one of skill in the art, thereceipt, demodulation of the alert message burst comprises: (1) SQRCmatched filtering (module 711); (2) timing and frequency compensationusing the synchronization tracking loop outputs (modules 713, 715, 717);(3) π/2 de-rotation and descrambling (module 719); (4) orthogonalsequence detection, jointly correlating all three sequences received inthe burst (modules 721, 723); (5) SNR estimation and decoder input wordgeneration, with one per Reed-Solomon symbol and three total (module725); and (6) buffering of three 4-bit words for every received alertmessage burst (module 727). By way of example, the following tablesummarizes the receiver parameters for alert message burst demodulationand decoding:

Module Parameter Values SQRC Matched Number of symbols in a burst: N =234 Filtering Roll-off factor: α = 0.35, Filter window size: (Module711) L = 8 symbols Number of samples per symbol: M = 4 Timing FromSynchronization Burst tracking Estimation (Module 715) InterpolationSynchronization Interpolator and Decimation Interpolation filter taplength: I = 16 (Module 713) Oversampling factor for interpolation: v = 8Frequency From Synchronization Burst tracking Estimation and Number ofsamples per symbol: M = 1 Compensation (Modules 715, 717) OrthogonalCorrelation is performed jointly across three Joint Sequence receivedsequences. To minimize processing Detection complexity, the jointdetection can be limited to (Module 721) total 5 candidates for eachreceived sequence segment, reducing the total number of hypothesis from16 × 16 × 16 to 5 × 5 × 5 in the burst. The five candidates for eachreceived sequence are determined by top five maximum correlationmagnitudes when the correlation is individually performed on singlesequence duration. RS Symbol SNR SNR estimation is performed for each RSsymbol, Estimation total three SNR estimates per burst. Number of(Module 725) symbols used in each SNR computation: 76 Soft Decision 4coded bits per RS symbol (Module 725) Three 4 decoded bits per burst

More specifically, for example, the three 16-ary sequences in the alertmessage burst may be jointly determined in the following manner:

$\left\{ {l_{1},l_{2},l_{3}} \right\} = {\underset{0 \leq {\{{j_{1},j_{2},j_{3}}\}} \leq 15}{\arg \; \max}\mspace{14mu}\left\lbrack {{S_{j_{1}}^{(1)} + S_{j_{2}}^{(2)} + S_{j_{3}}^{(3)}}}^{2} \right\rbrack}$

where S_(l) ^((k)) denotes a complex value obtained by correlating thek-th received sequence in the burst with the stored 16-ary sequence withindex l. Notice that the above optimum joint detection demandssignificant processing compared to each sequence is detectedindividually. To minimize processing complexity, the size of each indexin {j₁,j₂,j₃} is limited to total 5 sequence indexes that give the top 5maximum correlation magnitudes when the correlation is individuallyperformed on single sequence duration.

Decoding.

A Reed-Solomon (RS) decoder, for example, can be used to correct allcombinations of v symbol errors and e symbol erasures, provided that thefollowing inequality holds true: v+e/2≦t, where t is the errorcorrection capability of the RS code. For example, for a (15,9) RS code,t=3. All 15 words are used to compute the various intermediatecomputations so that the input stream must be completely read in tobegin the processing. By way of example, an iterative erasure-baseddecoding algorithm (e.g., generalized minimum distance (GMD) decoding)may be used for decoding, where the data is processed in 4-bit wordswith arithmetic operations performed in Galois field 2⁴ (GF(2⁴). GMDdecoding provides an efficient algorithm for decoding based on using anerrors and erasures decoder for the outer code, where a confidence foreach received codeword is determined and symbols exhibiting a confidencebelow a predetermined value are erased.

Iterative Erasure-Based Decoding:

FIG. 10A illustrates a flow chart depicting an iterative erasure-baseddecoding process, in accordance with an exemplary embodiment. By way ofexample, with an iterative erasure-based decoding, more than onecodeword is produced by iteratively running the RS decoder using 0, 2, .. . etc. erasures, and the algorithm then selects the most likelycodeword from an available set of determined candidate codewords. Withreference to FIG. 10A, the Reed-Solomon encoded symbols are firstreceived, and the SNR estimation per burst is used as a reliability orconfidence measure to determine the RS symbols to be erased at eachiteration (S1010). The iteration (ITER.) is set to 1 for the 1^(st)iteration (S1012). Next, a number of symbols with the lowest confidence(lowest SNR) are erased, where the number to be erased is two times theiteration number minus one (2*(ITER.−1)) (S1014). For example, for thefirst iteration, zero RS symbols are erased (2*(1−1)=0). Accordingly,the RS symbols exhibiting the lowest SNR are the first to be erasedpursuant to the algorithm. For the present iteration, a Euclidiandecoding algorithm for errors and erasures is then employed to produce adecoded codeword (S1016). Then, if no decoder failures occurred (S1018),the decoded codeword is stored as a candidate codeword (S1020). Also, ifthe iteration is less than 3 (S1022), then the iteration is incrementedby one (S1024), and the process returns to S1014. Alternatively, if theiteration equals 3 (S1022), then the codeword with the minimum Hammingdistance from the received sequence is selected (S1026).

As specified above, the (15,9) Reed-Solomon decoder can correct allcombinations of v symbol errors and e symbol erasures, provided that thefollowing inequality v+e/2≦t holds true. The following table lists thenumber of symbols to be erased by iteration number:

e Symbol v Symbol Iteration Erasures Errors Comments 1 0 3 ErrorCorrection Only/No erasure 2 2 2 3 4 1 Max iteration 4 6 0 Not usedAccordingly, because the decoding algorithm includes a maximum of 3iterations, the resulting decoded codeword candidate list can have nomore than three decoded codewords. The codeword that reflects the lowestHamming distance with respect to the hard decision received sequence ischosen as the decoded solution (S1026).

FIG. 10B illustrates a Reed-Solomon decoding process employing aconventional Euclidian algorithm, in accordance with an exemplaryembodiment. By way of example, considering a polynomial r(x), such thatthere are v symbol errors at positions X^(i) ¹ , X^(i) ² , . . . X^(i)^(v) and e symbol erasures at positions X^(j) ¹ , X^(j) ² , X^(j) ^(e) ,because the locations of the erased positions are known apriori,decoding achieves the locations and values of the errors and values ofthe erasures. The erasure location numbers corresponding to the erasedpositions at X^(j) ¹ , X^(j) ² , X^(j) ^(e) are α^(j) ¹ α^(j) ² , . . ., α^(j) ^(e) . The erasure polynomial can be represented by:

${\beta (x)} = {\prod\limits_{i = 1}^{e}\; \left( {1 - {\alpha^{j_{i}}X}} \right)}$

Further, the Euclidean algorithm for errors and erasures decodingfollows the following steps:

-   -   1. Compute the erasure location polynomial β(x) based on the        knowledge of the location of the erasures.    -   2. Form the modified received polynomial r*(x) by replacing the        erased symbols in the received polynomial by zeros.    -   3. Compute the syndromes S1 to S6, based on the modified        received polynomial r*(x).    -   4. Let T(x) be the modified syndrome polynomial—T(x)=[β(x)S(X)]        mod X⁶.    -   5. Set the following initial conditions:

Ω⁻¹(X)=X ⁶

Ω⁰(X)=T(X)

ζ⁻¹(X)=σ⁰(X)=1

ζ⁰(X)=σ⁻¹(X)=⁰

-   -   6. The Euclidian algorithm is then applied as described in the        previous section until a step k is reached, wherein:

deg Ω^(k)(X)<3+e/2 for even e

or

deg Ω^(k)(X)<3+(e−1)/2 for odd e

-   -   7. If k≦(2t−e), and the condition in step 6 is met, then set        Ω(X)=Ω^((k))(X) and σ(X)=Ω^((k))(X), otherwise declare a        decoding failure and stop decoding.    -   8. Find the roots of σ(X), and from there the error locations        can be obtained, as follows: If σ(α^(i))=0, then α^(i) is a root        of σ(X) and α^(15-i) is an error location number.    -   9. The values of the errors and erasures are then found using        Ω(X) and γ(X)=σ(X)β(X). Then, using Forney's equations the error        values are:

$e_{ik} = \frac{{- \Omega}\; \left( \alpha^{- i_{k}} \right)}{\gamma^{\prime}\left( \alpha^{- i_{k}} \right)}$

-   -   and the erasure values are:

$e_{jl} = \frac{{- \Omega}\; \left( \alpha^{- j_{l}} \right)}{\gamma^{\prime}\left( \alpha^{- j_{l}} \right)}$

-   -   where 1≦k≦v and 1≦l≦e.    -   10. If there are v error locations found then the error        polynomial can be written as:

${e(x)} = {\sum\limits_{k = 1}^{v}\; {e_{ik}X^{\alpha_{ik}}}}$

-   -   11. The decoded codeword is then v(x)=r*(x)−e(x).

Transmitter Performance

FIG. 11A illustrates a power spectrum density (PSD) plot 1110 of analert message burst which has been coded utilizing a Reed-Solomon outercoding and an orthogonal sequence with scrambling, in accordance with anexemplary embodiment. Further, FIG. 11B illustrates a power spectrumdensity (PSD) plot 1112 of an alert message burst which has been codedutilizing a Reed-Solomon outer coding (in accordance with an exemplaryembodiment) and a conventional orthogonal sequence without scrambling.As is evident from an analysis of PSD plot for the alert message burstdepicted in FIG. 11A, where the burst was coded with the application ofthe Reed-Solomon outer coding and orthogonal sequences with scrambling(in accordance with embodiments of the present invention) the PSD plotis regular and uniform. By contrast, the PSD plot for the alert messageburst depicted in FIG. 11B, where the burst was coded with theapplication of convention orthogonal sequences without scrambling,exhibits and uneven PSD. Hence, alert message bursts coded with theapplication of conventional orthogonal sequences are thus vulnerable toamplifier nonlinearity.

Moreover, the peak-to-Average-ratio (PAR) of alert message burstsmodulated based on a π/2 BPSK modulation scheme (in conjunction withscrambled binary orthogonal sequences), in accordance with exemplaryembodiments of the present invention, is about 1.84 dB, which issignificantly lower than that of alert message bursts modulated based onconventional PSK modulation (e.g., BPSK, QPSK, 6 PSK, MPSK). Moreover,compared to the 6 PSK modulation employed for alert message bursts incurrent mobile communications systems, the use of π/2 BPSK modulationreduces the PAR by more than 2 dB. This reduction in PAR facilitates asmaller amplifier back-off, and thus improved amplifier efficiency andimproved link margin in the system. A comparison of the PARs for signalsmodulated based on the π/2 BPSK modulation of embodiments of the presentinvention against signals based on such conventional modulation schemesis summarized in the following table:

Modu- π/2 PSK (BPSK, QPSK, π/4 16 16 lation BPSK 6 PSK, MPSK) QPSK QAMAPSK PAR (dB) 1.84 3.86 3.17 6.17 4.72

Receiver Performance

FIG. 11C illustrates a performance plot of a frequency tracking loopestimated RMS error in steady state 1114, where the tracking loop isimplemented in accordance with an exemplary embodiment of the presentinvention. Further, FIG. 11D illustrates a performance plot of a timingtracking loop estimated RMS error in steady state 1116, where thetracking loop is implemented in accordance with an exemplary embodiment.As can be seen from the plots, at an Es/No=−11 dB, the frequency RMSerror is less than 2.0 Hz and the timing RMS error is less than 3 μs, inan AWGN channel.

FIG. 11E illustrates a plot of the sequence error detection performance,over an AWGN channel, comparing the performance variations between theoptimal use of all 16 candidates in the joint detection against the useof 5 candidates and 3 candidates, in accordance with exemplaryembodiments. The use of fewer candidates reduces the computationalcomplexity and delay of the receiver. The plot illustrates theprobabilities of the receiver selecting a wrong sequence out of 16, 5and 3 candidates, which is reflected as symbol error probability (SER)and is equivalent to an RS symbol error rate before RS decoding.Further, the plots are shown under both ideal and practicalcircumstances, where ideal cases reflect an ideal receiver with notiming or frequency errors, and the practical cases reflect a receiverexhibiting residual timing and frequency errors (as illustrated in FIGS.11C and 11D). With reference to FIG. 11E, the plot 1118 depicts theoptimal case of 16 candidates under ideal conditions, the plot 1120depicts the case of 3 candidates under ideal conditions, the plot 1122depicts the case of 3 candidates under practical conditions, the plot1124 depicts the case of 5 candidates under ideal conditions, and theplot 1126 depicts the case of 5 candidates under practical conditions.As is evident from the plots, the performance difference between theoptimum (all 16 candidates) case and the case using 5 candidates in thejoint detection with ideal receiver is less than 0.1 dB in an AWGNchannel, and the performance difference between the case of using 5candidates and the case of using 3 candidates is less than another 0.1dB. Further, the difference between the practical and ideal situationsis very small, about 0.1 dB in an AWGN channel. As a result, the changefrom 16 down to 5 candidates in the joint detection algorithm results ina significant reduction in receiver complexity, while not sacrificingany significant level of performance, whereas a further reduction downto 3 candidates does not achieve any further significant reduction incomplexity to justify a further reduction in performance. Accordingly,employment of the transmission waveform and the receiver joint detectionalgorithms in accordance with exemplary embodiments of the presentinvention facilitates the use of fewer candidates in the joint detectionalgorithm (e.g., 5 candidates), without a significant sacrifice inperformance, which results in a significant reduction in receivercomplexity.

FIG. 11F illustrates a plot of the alert message error performance in anAWGN channel, comparing the alert message error rates between anexemplary embodiment and the conventional alert messaging approach. Thealert message error rate performance depicted in FIG. 11F reflects animplementation in accordance with exemplary embodiments of the presentinvention, employing a practical joint sequence detection and iterativeerror & erasure RS decoder up to 4 erasures. With reference to FIG. 11F,for example, a message error rate of 5% is achieved at a received Es/Noof −11.3 dB. Further, as depicted in FIG. 11F, the enhancement inmessage error performance achieved by the alerting approaches ofexemplary embodiments of the present invention is about 1.3 dB betterthan that of current systems. Moreover, considering the PAR advantagemore than 2 dB (described above), embodiments of the present inventionachieve a net link margin gain of more than 3.3 dB.

FIG. 12 illustrates a block diagram of exemplary components of a userterminal configured to operate in the systems of FIGS. 1 and 2,according to an exemplary embodiment. A user terminal 1200 includes anantenna system 1201 (which can utilize multiple antennas) to receive andtransmit signals. The antenna system 1201 is coupled to radio circuitry1203, which includes multiple transmitters 1205 and receivers 1207. Theradio circuitry encompasses all of the Radio Frequency (RF) circuitry aswell as base-band processing circuitry. As shown, layer-1 (L1) andlayer-2 (L2) processing are provided by units 1209 and 1211,respectively. Optionally, layer-3 functions can be provided (not shown).Module 1213 executes all Medium Access Control (MAC) layer functions. Atiming and calibration module 1215 maintains proper timing byinterfacing, for example, an external timing reference (not shown).Additionally, a processor 1217 is included. Under this scenario, theuser terminal 1200 communicates with a computing device 1219, which canbe a personal computer, work station, a Personal Digital Assistant(PDA), web appliance, cellular phone, etc.

FIG. 13 illustrates a chip set 1300 with respect to which embodiments ofthe invention may be implemented. Chip set 1300 includes, for instance,processor and memory components described with respect to FIG. 13incorporated in one or more physical packages. By way of example, aphysical package includes an arrangement of one or more materials,components, and/or wires on a structural assembly (e.g., a baseboard) toprovide one or more characteristics such as physical strength,conservation of size, and/or limitation of electrical interaction.

In one embodiment, the chip set 1300 includes a communication mechanismsuch as a bus 1301 for passing information among the components of thechip set 1300. A processor 1303 has connectivity to the bus 1301 toexecute instructions and process information stored in, for example, amemory 1305. The processor 1303 includes one or more processing coreswith each core configured to perform independently. A multi-coreprocessor enables multiprocessing within a single physical package.Examples of a multi-core processor include two, four, eight, or greaternumbers of processing cores. Alternatively or in addition, the processor1303 includes one or more microprocessors configured in tandem via thebus 1301 to enable independent execution of instructions, pipelining,and multithreading. The processor 1303 may also be accompanied with oneor more specialized components to perform certain processing functionsand tasks such as one or more digital signal processors (DSP) 1307,and/or one or more application-specific integrated circuits (ASIC) 1309.A DSP 1307 typically is configured to process real-world signals (e.g.,sound) in real time independently of the processor 1303. Similarly, anASIC 1309 can be configured to performed specialized functions noteasily performed by a general purposed processor. Other specializedcomponents to aid in performing the inventive functions described hereininclude one or more field programmable gate arrays (FPGA) (not shown),one or more controllers (not shown), or one or more otherspecial-purpose computer chips.

The processor 1303 and accompanying components have connectivity to thememory 1305 via the bus 1301. The memory 1305 includes both dynamicmemory (e.g., RAM) and static memory (e.g., ROM) for storing executableinstructions that, when executed by the processor 1303 and/or the DSP1307 and/or the ASIC 1309, perform the process of exemplary embodimentsas described herein. The memory 1305 also stores the data associatedwith or generated by the execution of the process.

FIG. 14 illustrates a block diagram of exemplary hardware that can beused to implement certain exemplary embodiments. A computing system 1400includes a bus 1401 or other communications mechanism for communicatinginformation and a processor 1403 coupled to the bus 1401 for processinginformation. The computing system 1400 also includes main memory 1405,such as a random access memory (RAM) or other dynamic storage device,coupled to the bus 1401 for storing information and instructions to beexecuted by the processor 1403. Main memory 1405 can also be used forstoring temporary variables or other intermediate information duringexecution of instructions by the processor 1403. The computing system1400 may further include a read only memory (ROM) 1407 or other staticstorage device coupled to the bus 1401 for storing static informationand instructions for the processor 1403. A storage device 1409, such asa magnetic disk or optical disk, is coupled to the bus 1401 forpersistently storing information and instructions.

The computing system 1400 may be coupled via the bus 1401 to a display1411, such as a liquid crystal display, or active matrix display, fordisplaying information to a user. An input device 1413, such as akeyboard including alphanumeric and other keys, may be coupled to thebus 1401 for communicating information and command selections to theprocessor 1403. The input device 1413 can include a cursor control, suchas a mouse, a trackball, or cursor direction keys, for communicatingdirection information and command selections to the processor 1403 andfor controlling cursor movement on the display 1411.

According to various embodiments of the invention, the processesdescribed herein can be provided by the computing system 1400 inresponse to the processor 1403 executing an arrangement of instructionscontained in main memory 1405. Such instructions can be read into mainmemory 1405 from another computer-readable medium, such as the storagedevice 1409. Execution of the arrangement of instructions contained inmain memory 1405 causes the processor 1403 to perform the process stepsdescribed herein. One or more processors in a multi-processingarrangement may also be employed to execute the instructions containedin main memory 1405. In alternative embodiments, hard-wired circuitrymay be used in place of or in combination with software instructions toimplement the embodiment of the invention. In another example,reconfigurable hardware such as Field Programmable Gate Arrays (FPGAs)can be used, in which the functionality and connection topology of itslogic gates are customizable at run-time, typically by programmingmemory look up tables. Thus, embodiments of the invention are notlimited to any specific combination of hardware circuitry and software.

The computing system 1400 also includes at least one communicationsinterface 1415 coupled to bus 1401. The communications interface 1415provides a two-way data communications coupling to a network link (notshown). The communications interface 1415 sends and receives electrical,electromagnetic, or optical signals that carry digital data streamsrepresenting various types of information. Further, the communicationsinterface 1415 can include peripheral interface devices, such as aUniversal Serial Bus (USB) interface, a PCMCIA (Personal Computer MemoryCard International Association) interface, etc.

The processor 1403 may execute the transmitted code while being receivedand/or store the code in the storage device 1409, or other non-volatilestorage for later execution. In this manner, the computing system 1400may obtain application code in the form of a carrier wave.

The term “computer-readable medium” as used herein refers to any mediumthat participates in providing instructions to the processor 1403 forexecution. Such a medium may take many forms, including but not limitedto non-volatile media, volatile media, and transmission media.Non-volatile media include, for example, optical or magnetic disks, suchas the storage device 1409. Volatile media include dynamic memory, suchas main memory 1405. Transmission media include coaxial cables, copperwire and fiber optics, including the wires that comprise the bus 1401.Transmission media can also take the form of acoustic, optical, orelectromagnetic waves, such as those generated during radio frequency(RF) and infrared (IR) data communications. Common forms ofcomputer-readable media include, for example, a floppy disk, a flexibledisk, hard disk, magnetic tape, any other magnetic medium, a CD-ROM,CDRW, DVD, any other optical medium, punch cards, paper tape, opticalmark sheets, any other physical medium with patterns of holes or otheroptically recognizable indicia, a RAM, a PROM, and EPROM, a FLASH-EPROM,any other memory chip or cartridge, a carrier wave, or any other mediumfrom which a computer can read.

Various forms of computer-readable media may be involved in providinginstructions to a processor for execution. For example, the instructionsfor carrying out at least part of the invention may initially be borneon a magnetic disk of a remote computer. In such a scenario, the remotecomputer loads the instructions into main memory and sends theinstructions over a telephone line using a modem. A modem of a localsystem receives the data on the telephone line and uses an infraredtransmitter to convert the data to an infrared signal and transmit theinfrared signal to a portable computing device, such as a personaldigital assistant (PDA) or a laptop. An infrared detector on theportable computing device receives the information and instructionsborne by the infrared signal and places the data on a bus. The busconveys the data to main memory, from which a processor retrieves andexecutes the instructions. The instructions received by main memory canoptionally be stored on storage device either before or after executionby processor.

According to the preceding, various exemplary embodiments have beendescribed with reference to the accompanying drawings. The exampleembodiments, as described above, were chosen and described in order tobest explain the principles of the invention and its practicalapplication to thereby enable others skilled in the art to best utilizethe invention in various embodiments and with various modifications asare suited to the particular use contemplated. The specification anddrawings are accordingly to be regarded in an illustrative rather thanrestrictive sense. Moreover, it will be evident that variousmodifications and changes may be made thereto, and additionalembodiments may be implemented, without departing from the broader scopeof the invention.

What is claimed is:
 1. A method comprising: generating, by a processor,a message for transmission to a wireless terminal, wherein the messagecomprises a number of bits; partitioning the message into a number ofsymbols, each symbol being composed of a distinct equal length portionof the message; encoding the symbols via an FEC outer coding to generatea number of outer coded symbols; encoding each of the outer codedsymbols based on an orthogonal sequence inner coding to generate arespective inner coded symbol, wherein each outer coded symbol is codedbased on a distinct corresponding one of a plurality of binaryorthogonal sequences; and modulating the inner coded symbols based on abinary modulation scheme, and pulse shaping the modulated inner codedsymbols to generate a plurality of message bursts for transmission tothe wireless terminal; and wherein each message burst reflects a groupof a uniform number of the inner coded symbols, wherein the grouping ofthe inner coded symbols within the message bursts facilitates jointsequence detection by a receiver of the wireless terminal, and whereineach message burst exhibits relatively low peak-to-average power ratio.2. The method of claim 1, wherein the binary modulation scheme comprisesone of binary phase shift keying (BPSK), π/2 BPSK, quadrature phaseshift keying (QPSK), and offset quadrature phase shift keying (OQPSK).3. The method of claim 1, wherein the encoding of the outer codedsymbols further comprises scrambling each message burst based on abinary scrambling sequence.
 4. The method of claim 1, wherein thedistinct corresponding binary orthogonal sequence, based upon which eachouter coded symbol is encoded, is based on a value of the respectiveouter coded symbol.
 5. The method of claim 4, wherein each outer codedsymbol is four bits in length, and the orthogonal sequence inner codingcomprises a 16-ary coding based on sixteen binary orthogonal sequenceswith each sequence corresponding to a respective one of the potentialfour-bit values of the outer coded symbols.
 6. The method of claim 5,wherein the sixteen four-bit value outer coded symbol values andcorresponding binary orthogonal sequences are as follows: 4-Bit OuterCoded Symbol Value Binary Orthogonal Sequences (76 elements perSequence) 00000001001100001111001100000000111111001111111100111111000000001100111100001100000100110001001100001111001100000000111111001111111100111111000000001100111100000010000000110001001100001111001100000000111111001111111100111111000000001100111100110011110000110001001100001111001100000000111111001111111100111111000000001100010000110011110000110001001100001111001100000000111111001111111100111111000000000101000000110011110000110001001100001111001100000000111111001111111100111111000001100000000000110011110000110001001100001111001100000000111111001111111100111111011100111100000000110011110000110001001100001111001100000000111111001111111100111000111100000011111111001100001111001110110011110000110011111111000000110000000010011100001100000011111111001100001111001110110011110000110011111111000000110000101011000000001100000011111111001100001111001110110011110000110011111111000000111011110011000000001100000011111111001100001111001110110011110000110011111111000011001100000011000000001100000011111111001100001111001110110011110000110011111111110111111100000011000000001100000011111111001100001111001110110011110000110011111110111111111100000011000000001100000011111111001100001111001110110011110000110011111111001111111100000011000000001100000011111111001100001111001110110011110000


7. The method of claim 6, wherein the encoding of the outer codedsymbols further comprises scrambling each message burst based on a228-bit binary scrambling sequence, as follows:000100110001101111000100001001010000111110001100000101011110111111001101011010101110110010011001011011100010001101101000011110110110000010100100100000011000111000000010000101111111100000110101010111111011001100101010010001000110.
 8. The method ofclaim 7, wherein the message comprises 36 information bits, the messageis partitioned into nine 4-bit symbols, the FEC outer coding generatesfifteen 4-bit outer coded symbols, and each message burst reflects agroup of three of the inner coded symbols.
 9. The method of claim 8,wherein the binary modulation scheme comprises a π/2 BPSK scheme appliedas follows:S _(l)=(−1)^(d) ^(l) *e ^(jl(π/2)) where d_(l) denotes the scrambledbits, and S_(l) denotes the π/2 BPSK modulated symbol, and the outercoding comprises a Reed-Solomon (15,9) outer code, with a Galois fieldof 2⁴ (GF(2⁴)).
 10. An apparatus comprising: a processor moduleconfigured to generate a message for transmission to a wirelessterminal, wherein the message comprises a number of bits, and topartition the message into a number of symbols, each symbol beingcomposed of a distinct equal length portion of the message; an encodermodule configured to encode the symbols via an FEC outer coding togenerate a number of outer coded symbols, and to encode each of theouter coded symbols based on an orthogonal sequence inner coding togenerate a respective inner coded symbol, wherein each outer codedsymbol is coded based on a distinct corresponding one of a plurality ofbinary orthogonal sequences; and a modulator module configured tomodulate the inner coded symbols based on a binary modulation scheme;and one or more pulse shaping filters to pulse shape the modulated innercoded symbols to generate a plurality of message bursts for transmissionto the wireless terminal; and wherein each message burst reflects agroup of a uniform number of the inner coded symbols, wherein thegrouping of the inner coded symbols within the message burstsfacilitates joint sequence detection by a receiver of the wirelessterminal, and wherein each message burst exhibits relatively lowpeak-to-average power ratio.
 11. The apparatus of claim 10, wherein thebinary modulation scheme comprises one of binary phase shift keying(BPSK), π/2 BPSK, quadrature phase shift keying (QPSK), and offsetquadrature phase shift keying (OQPSK).
 12. The apparatus of claim 10,wherein, as part of the encoding of the outer coded symbols, the encoderis further configured to scramble each message burst based on a binaryscrambling sequence.
 13. The apparatus of claim 10, wherein the distinctcorresponding binary orthogonal sequence, based upon which each outercoded symbol is encoded, is based on a value of the respective outercoded symbol.
 14. The apparatus of claim 13, wherein each outer codedsymbol is four bits in length, and the orthogonal sequence inner codingcomprises a 16-ary coding based on sixteen binary orthogonal sequenceswith each sequence corresponding to a respective one of the potentialfour-bit values of the outer coded symbols.
 15. The apparatus of claim14, wherein the sixteen four-bit value outer coded symbol values andcorresponding binary orthogonal sequences are as follows: 4-Bit OuterCoded Symbol Value Binary Orthogonal Sequences (76 elements perSequence) 00000001001100001111001100000000111111001111111100111111000000001100111100001100000100110001001100001111001100000000111111001111111100111111000000001100111100000010000000110001001100001111001100000000111111001111111100111111000000001100111100110011110000110001001100001111001100000000111111001111111100111111000000001100010000110011110000110001001100001111001100000000111111001111111100111111000000000101000000110011110000110001001100001111001100000000111111001111111100111111000001100000000000110011110000110001001100001111001100000000111111001111111100111111011100111100000000110011110000110001001100001111001100000000111111001111111100111000111100000011111111001100001111001110110011110000110011111111000000110000000010011100001100000011111111001100001111001110110011110000110011111111000000110000101011000000001100000011111111001100001111001110110011110000110011111111000000111011110011000000001100000011111111001100001111001110110011110000110011111111000011001100000011000000001100000011111111001100001111001110110011110000110011111111110111111100000011000000001100000011111111001100001111001110110011110000110011111110111111111100000011000000001100000011111111001100001111001110110011110000110011111111001111111100000011000000001100000011111111001100001111001110110011110000


16. The apparatus of claim 15, wherein, as part of the encoding of theouter coded symbols, the encoder is further configured to scramble eachmessage burst based on a 228-bit binary scrambling sequence, as follows:000100110001101111000100001001010000111110001100000101011110111111001101011010101110110010011001011011100010001101101000011110110110000010100100100000011000111000000010000101111111100000110101010111111011001100101010010001000110.
 17. The apparatusof claim 16, wherein the message comprises 36 information bits, themessage is partitioned into nine 4-bit symbols, the FEC outer codinggenerates fifteen 4-bit outer coded symbols, and each message burstreflects a group of three of the inner coded symbols.
 18. The apparatusof claim 17, wherein the binary modulation scheme comprises a π/2 BPSKscheme applied as follows:S _(l)=(−1)^(d) ^(l) *e ^(jl(π/2)) where d_(l) denotes the scrambledbits, and S_(l) denotes the π/2 BPSK modulated symbol, and the outercoding comprises a Reed-Solomon (15,9) outer code, with a Galois fieldof 2⁴ (GF(2⁴)).